Non-ergodic delocalization in the Rosenzweig–Porter model

Non-linear ergodic theorems in complete non-positive curvature metric spaces

Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...

Quantization of the Hall Conductance and Delocalization in Ergodic Landau Hamiltonians

We prove quantization of the Hall conductance for continuous ergodic Landau Hamiltonians under a condition on the decay of the Fermi projections. This condition and continuity of the integrated density of states are shown to imply continuity of the Hall conductance. In addition, we prove the existence of delocalization near each Landau level for these two-dimensional Hamiltonians. More precisel...

Credal and pignistic reasoning in ergodic and non-ergodic texts

This paper discusses the difference between ergodic and non-ergodic texts by considering the different levels of reasoning required of an agent in each case. The difference indentified between such texts is based on the distinction between credal and pignistic reasoning in the transferable belief model. It is argued that non-ergodic texts require an active agent to reason about the state of the...

Non-Gaussian normal diffusion induced by delocalization.

Non-Gaussian normal diffusion, i.e., the probability density function (PDF) is non-Gaussian but the mean squared displacement (MSD) depends on time linearly, has been observed in particle motions. Here we show by numerical simulations that this phenomenon may manifest itself in energy diffusion along a lattice at a nonzero, finite temperature. The studied model is a one-dimensional disordered l...

Ergodic Optimization for Non - Compactdynamical